Modern image classification methods are based on supervised learning algorithms that require labeled training data. However, only a limited amount of annotated data may be available in certain applications due to scarcity of the data itself or high costs associated with human annotation. Introduction of additional information and structural constraints can help improve the performance of a learning algorithm. In this thesis, we study the framework of learning using privileged information and demonstrate its relation to learning with instance weights. We also consider multitask feature learning and develop an efficient dual optimization scheme that is particularly well suited to problems with high dimensional image descriptors. Scaling annotation to a large number of image categories leads to the problem of class ambiguity where clear distinction between the classes is no longer possible. Many real world images are naturally multilabel yet the existing annotation might only contain a single label. In this thesis, we propose and analyze a number of loss functions that allow for a certain tolerance in top k predictions of a learner. Our results indicate consistent improvements over the standard loss functions that put more penalty on the first incorrect prediction compared to the proposed losses. All proposed learning methods are complemented with efficient optimization schemes that are based on stochastic dual coordinate ascent for convex problems and on gradient descent for nonconvex formulations.